BAKER HUGHES - Drilling Fluids Reference Manual

Hydraulics
Reynolds showed further that under some circumstances, the flow can alternate back and forth
between being laminar and turbulent. When that happens, it is called transitional flow.
Therefore, we can describe a fluid's flow as being either laminar, turbulent, or transitional.
Additionally, another term has been used to describe a fluid's flow at extremely low flow rates – plug
flow.
The particular flow regime of a drilling fluid during drilling operations can have a dramatic effect on
parameters such as pressure losses, hole cleaning, and hole stability.
Plug Flow
In plug flow, the fluid moves essentially as a single, undisturbed solid body. Movement of the fluid
occurs due to the slippage of a very thin layer of fluid along the pipe wall or conductor surface. Plug
flow generally occurs only at extremely low flow rates.
Laminar Flow
The laminar flow of a Newtonian liquid in a circular pipe is illustrated in Figure 1-2. Laminar flow of
a Newtonian fluid can be visualized as concentric cylindrical shells which slide past one another like
sections of a telescope. The velocity of the shell at the pipe wall is zero, and the velocity of the shell
at the center of the pipe is the greatest.
Figure 1-2
Three Dimension View of Laminar Flow in a Pipe for a Newtonian Fluid
A two-dimensional velocity profile is illustrated in Figure 1-3. The shear rate, previously defined as
the velocity difference between two layers of fluid divided by the difference between the two layers,
is simply the slope of a line at any point along the velocity profile. The shear rate is greatest at the
wall and zero at the center of the pipe. Since the shear stress and shear rate for a Newtonian fluid are
directly proportional, the shear stress is also greatest at the wall and zero at the center of the pipe.
Figure 1-3
Two/Three Dimensional Velocity Profile of Laminar Flow in a Pipe for a Newtonian
Fluid
The laminar flow of a non-Newtonian fluid is very similar to that of a Newtonian fluid with the
exception that some portion of the cylindrical shells in the center of a pipe may not slide past one
another.
Reference Manual
Baker Hughes Drilling Fluids
1-8 Revised 2006